Which function has an inverse function?
/=means the _ of a fraction like 4
_
5
f(x)= [x+3]/5

f(x)=x^5-3

f(x)=x^4/7 +27

f(x)=1/x^2

The correct option is 2.

Step-by-step explanation:

A function has an inverse function if and only if it is a one-to-one function. It means for each value of x there exist a unique value of y.

In option 1,

It is an absolute function. For each value of x there axis more than 1 value of f(x). Therefore this function does not has an inverse function.

In option 2,

The degree of the function is 5 which is an odd number. Therefore it is a one-to-one function. Therefore this function has an inverse function.

In option 3,

The degree of the function is 4 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

In option 4,

The degree of the function is 2 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

Hence option 2 is correct.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.